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A252659 Numbers m such that 6^m - m is a semiprime. 2


%S 2,3,5,10,15,23,34,37,47,70

%N Numbers m such that 6^m - m is a semiprime.

%C From _Robert Israel_, Sep 06 2016: (Start)

%C Even n is in this sequence iff (6^n-n)/2 is prime.

%C 3*k is in this sequence iff (2*6^(3*k-1)-k is prime.

%C Also contains 275, 278 and 683.

%C The only other possible member less than 275 is 259. (End)

%e 2 is in this sequence because 6^2-2 = 2*17 is semiprime.

%e 10 is in this sequence because 6^10-10 = 2*30233083 and these two factors are prime.

%p Res:= NULL:

%p for n from 1 to 100 do

%p F:= ifactors(6^n-n, easy)[2];

%p if add(t[2], t=F) >= 3 or (hastype(F, symbol) and add(t[2], t=F) >= 2)

%p then flag:= false

%p elif add(t[2], t=F) = 2 and not hastype(F, symbol) then flag:= true

%p else

%p flag:= evalb(numtheory:-bigomega(6^n-n)=2)

%p fi;

%p if flag then Res:= Res, n fi

%p od:

%p Res; # _Robert Israel_, Sep 06 2016

%t Select[Range[90], PrimeOmega[6^# - #]== 2&]

%o (MAGMA) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [m: m in [1..90] | IsSemiprime(s) where s is 6^m-m];

%Y Cf. similar sequences listed in A252656.

%K nonn,more

%O 1,1

%A _Vincenzo Librandi_, Dec 21 2014

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Last modified May 10 22:16 EDT 2021. Contains 343780 sequences. (Running on oeis4.)